chosen ciphertext attack (CCA) security on the standard model is widely accepted as the standard security notion for the public key cryptosystem.The existing CCA-secure public key cryptosystems on the standard model are expensive in terms of efficiency and practicality.In this paper,an efficient and practical public key cryptosystem is presented over the group of signed quadratic residues.It is provably secure against CCA on the standard model.Furthermore,publicly verifiability for the scheme is also realized in the way that projects the privacy key into public key on trapdoor pretending.It will be useful to devise efficient CCA-secure threshold and proxy re-encryption schemes on the standard model.